Question: s involving definite integrals (algebraic) AP.CALC: CHA‑4 (EU), CHA‑4.D (LO), CHA‑4.D.1 (EK), CHA‑4.D.2 (EK), CHA‑4.E (LO), CHA‑4.E.1 (EK) Google Classroom Facebook Twitter Email You might need: Calculator Problem As an infant, Naveen gained mass at a rate of $\dfrac{2.6}{t}$ kilograms per month (where $t$ was Naveen's age in months). By how many kilograms did Naveen's mass increase between $t=5$ and $t=10$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $2.6\ln(2)$ (Choice B) B $2.6\ln(5)$ (Choice C) C $2.6\ln(10)$ (Choice D) D $2.6\ln(15)$
Explanation: Letting $m(t)$ be Naveen's mass at month $t$, we are given that $m'(t)=\dfrac{2.6}{t}$. We want to find $m(10)-m(5)$. According to the Fundamental Theorem of Calculus, $\begin{aligned} m(10)-m(5)&=\int_{5}^{10} m'(t)\,dt \\\\ &=\int_{5}^{10}\left(\dfrac{2.6}{t}\right)dt \end{aligned}$ $\int_{5}^{10}\left(\dfrac{2.6}{t}\right)dt=2.6\ln(2)$ In conclusion, between $t=5$ and $t=10$, Naveen's mass increased by $2.6\ln(2)$ kilograms.